2(7x-3)-9=6x(2x-5)+10

Solution for 2(7x-3)-9=6x(2x-5)+10 equation:

Simplifying
2(7x + -3) + -9 = 6x(2x + -5) + 10

Reorder the terms:
2(-3 + 7x) + -9 = 6x(2x + -5) + 10
(-3 * 2 + 7x * 2) + -9 = 6x(2x + -5) + 10
(-6 + 14x) + -9 = 6x(2x + -5) + 10

Reorder the terms:
-6 + -9 + 14x = 6x(2x + -5) + 10

Combine like terms: -6 + -9 = -15
-15 + 14x = 6x(2x + -5) + 10

Reorder the terms:
-15 + 14x = 6x(-5 + 2x) + 10
-15 + 14x = (-5 * 6x + 2x * 6x) + 10
-15 + 14x = (-30x + 12x2) + 10

Reorder the terms:
-15 + 14x = 10 + -30x + 12x2

Solving
-15 + 14x = 10 + -30x + 12x2

Solving for variable 'x'.

Reorder the terms:
-15 + -10 + 14x + 30x + -12x2 = 10 + -30x + 12x2 + -10 + 30x + -12x2

Combine like terms: -15 + -10 = -25
-25 + 14x + 30x + -12x2 = 10 + -30x + 12x2 + -10 + 30x + -12x2

Combine like terms: 14x + 30x = 44x
-25 + 44x + -12x2 = 10 + -30x + 12x2 + -10 + 30x + -12x2

Reorder the terms:
-25 + 44x + -12x2 = 10 + -10 + -30x + 30x + 12x2 + -12x2

Combine like terms: 10 + -10 = 0
-25 + 44x + -12x2 = 0 + -30x + 30x + 12x2 + -12x2
-25 + 44x + -12x2 = -30x + 30x + 12x2 + -12x2

Combine like terms: -30x + 30x = 0
-25 + 44x + -12x2 = 0 + 12x2 + -12x2
-25 + 44x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-25 + 44x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
2.083333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -3.666666667x + -2.083333333 + x2 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -3.666666667x + x2 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + -2.083333333
-3.666666667x + x2 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-3.666666667x + x2 = -2.083333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -2.083333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -2.083333333 + 3.361111114

Combine like terms: -2.083333333 + 3.361111114 = 1.277777781
3.361111114 + -3.666666667x + x2 = 1.277777781

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 1.277777781

Calculate the square root of the right side: 1.130388332

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.130388332 and -1.130388332.

Subproblem 1
x + -1.833333334 = 1.130388332

Simplifying
x + -1.833333334 = 1.130388332

Reorder the terms:
-1.833333334 + x = 1.130388332

Solving
-1.833333334 + x = 1.130388332

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.130388332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.130388332 + 1.833333334
x = 1.130388332 + 1.833333334

Combine like terms: 1.130388332 + 1.833333334 = 2.963721666
x = 2.963721666

Simplifying
x = 2.963721666

Subproblem 2
x + -1.833333334 = -1.130388332

Simplifying
x + -1.833333334 = -1.130388332

Reorder the terms:
-1.833333334 + x = -1.130388332

Solving
-1.833333334 + x = -1.130388332

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.130388332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.130388332 + 1.833333334
x = -1.130388332 + 1.833333334

Combine like terms: -1.130388332 + 1.833333334 = 0.702945002
x = 0.702945002

Simplifying
x = 0.702945002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.963721666, 0.702945002}